Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties

@article{AriasdeReyna2013CompatibleSO,
  title={Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties},
  author={Sara Arias-de-Reyna and Luis V. Dieulefait and Sug Woo Shin and Gabor Wiese},
  journal={Mathematische Annalen},
  year={2013},
  volume={361},
  pages={909-925}
}
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer $$n$$n and any positive integer $$d$$d, $$\mathrm {PSp}_n(\mathbb {F}_{\ell ^d})$$PSpn(Fℓd) or $$\mathrm {PGSp}_n(\mathbb {F}_{\ell ^d})$$PGSpn(Fℓd) occurs as a Galois group over the rational… 
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16 Citations
Background Citations
3
Methods Citations
1
Results Citations
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16 Citations

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Galois Representations and Galois Groups Over Q
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Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image.
This article is the second part of a series of three articles a bout compatible systems of symplectic Galois representations and applications to the inv erse Galois problem. This part is concerned…
On the images of the Galois representations attached to certain RAESDC automorphic representations of GL n ( A Q )
In the 80’s Aschbacher classified the maximal subgroups of almost all of the finite almost simple classical groups. Essentially, this classification divide these subgroups into two types. The first…
Constructing Self-Dual Automorphic Representations on General Linear Groups
We prove a globalization theorem for self-dual representations of GLN over a totally real number field F, which gives a positive existence criterion for self-dual cuspidal automorphic representations…
Langlands Correspondence and Constructive Galois Theory
Recent progress in the Langlands programm provides a significant step towards the understanding of the arithmetic of global fields. The geometric Langlands program provides a systematic way to…
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References

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Compatible systems of symplectic Galois representations and the inverse Galois problem
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves…
Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we…
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